Tides, which are typically observed along the coasts are the periodic, usually
twice daily, rise and fall of the ocean resulting
from
gravitational
interactions of the
moon, sun
and the earth. Although gravity provides the driving force behind tides,
the rotation of the earth, size and geometry of ocean basins, and local climatic
conditions play an important role in determining the local magnitude and peroidicity
of tides.

Significance of tides

Tides are responsible for moving large
amounts of sediment perpendicular to the coast

Tidal range governs the width of the
littoral zone.

The periodic rise and fall varies the
distribution of wave energy along the beach profile

Gravitational Force: The force of attraction between
masses. The force is proportional to the masses of the bodies
being considered and inversely proportional to the square of the
distance between them:

Therefore the moon, which is 390x
closer than the sun, produces a greater tide force than the sun, even
though its
mass is much less. However the force produced by the sun is still significant.

The gravitational force of the
moon is directed in a line pointing toward the moon. The same applies
for the sun.

Centrifugal Force: An apparent "center-fleeing
force" felt by objects experiencing uniform circular motion.
This "force" is the result of inertial resistance to
centripetal acceleration.

Produced by the
revolving of the earth and moon around a common center of mass, which
is located approximately
1700 km
beneath the earths surface.

Centrifugal force is equally felt on all points of the earth and is
directed away from the moon along a line that parallels a hypothetical
line joining
the centers of the Earth and the Moon.

Coriolis Force: An apparent
force caused by the rotation of the earth, which is responsible
for the deflection
of surface currents toward the right in the northern hemisphere
and to the left in the southern hemisphere (Diagram and movie from
Topex/Poseidon online
tutorial). The Coriolis force plays an important role in the formation
of rotating standing waves (kelvin waves) in basins. (Discussed
later)

Equilibrium Theory of Tide Formation

Newton described the effects of tide generating forces on a theoretical
earth covered by an ocean of uniform depth and containing no
continents.

Two tidal bulges are produced on opposite
sides of the earth. The bulge facing the moon is produced largely by the
gravitational
effect of the moon. The bulge on the opposite side is produced by
centripital acceleration (centrifugal force).

The centrifugal force felt at
each point on the earth is uniform whereas the lunar G force decreases as
a function of
distance squared. The total force felt at any point on the earth is the
vector sum of these two forces. However, forces directed outward and perpendicular
to the Earth's surface are counteracted by the Earth's gravitational field.
The bulges are actually the result of the tractive (horizontal component)
force that draws the water toward them. In determining tides one also needs
to consider the influence of the Sun's gravitation force and the the fact
that distances of
the Moon
and
Sun
vary
relative
to the Earth.

The daily variations in high
and low tide results from the revolution of the earth beneath these these
bulges
at an angle
of 28°, the angle of tilt of the earths axis relative
to the moons orbital axis.

The monthly variations are
caused by the effects of the gravitational attraction of the sun which
either increases or decreases the tidal bulges produced by the
moon. [More about phases
if the Moon]

Spring Tides (bimonthly high
tides) occur during the full and new moon phase, when the moon and sun
are
aligned

Neap Tides (bimonthly
low tides) occur at half moon when the sun and moon are oriented at 90°.

Exercise: Go to the moon
phase calendar and make a plots for September and
October 2003. On each plot mark the occurrence of the Spring and
Neap tides.

Other variations:

Astronomical

Eccentricity of the moon's orbit
(27.55 day periodicity) varies the distance between the Moon and the
Earth. Slightly lower tides occur at apogee (407,
000 km) and higher tides at
perigee (357, 000 km).

Tilt of the Earth in relation to
the sun affects the magnitude of the spring tides.
The greatest difference in bulges occurs when the northern hemisphere
is inclined toward
or directly away from the sun.

Equinoxes (Sept 21 and
March 21) spring tides are highest because the Moon-Earth-Sun lie
along a straight
line.

Solstices (June 21 and Dec 21) spring tides are
lower because the Moon-Earth-Sun do not lie along a straight
line.

Proximity to the sun: the sun is closer
(perihelion:148,500,000 km) during our northern
winter and furthest (aphelion: 152,200,000 km) during
our Summer.

Dynamic Theory of Tides

The predicted equilibrium tides do not accurately
correspond to observed tides because:

Ocean basins average 4 km deep; too shallow
(c2=gd)
Problem: Compute the ocean depth
required to maintain an equilibrium tide. (C=40,000 km) How does this compare
with an average depth of 4 km?

Land masses prevent tidal bulges from
circumnavigating the globe causing the wave to become trapped
and reflected

Tidal flows are deflected by the Coriolis
force
causing tidal waves to rotate around the basin (cw-NH;
cc-SH)

The dynamic theory considers the configuration of the ocean
basins, frictional forces, Coriolis force, convergence and
resonance, and many other variables.

Terminology related to the dynamic theory

Amphidromic system: That region under the influence
of a single rotating (kelvin) wave. Kelvin waves rotation
counterclockwise in the northern hemisphere.

Amphidromic Point: The nodal point around which the
kelvin wave rotates. Tidal range at the amphidromic point is 0
and increases with distance away from it.

Cotidal lines: Lines connecting points experiencing
the high tide at the same time.

Corange Lines: Lines connecting
points having the same tidal range.

Questions:

1. In which hemisphere is the system shown above?

2. What are the lines in the diagram to the right?

Harmonic Method of Tide Prediction

The observed tide is produced
from a number of components (partial tides) having a given periodicity, amplitude
and phase
that can be represented by a sine wave. Each component is
determined by the harmonic analysis of a record taken from a gaging station
over a period of a year or more. Addition of all these components
enables an accurate prediction of future tides.

In the past decade sea surface elevations have been accurately
measured from the TOPEX/Poseidon and Jason-1 satellites.
These satellites contain altimeters that pulse microwaves toward
the surface of the ocean and
measure the time it takes the pulse to return. The distance obtained
is then subtracted from either the distance from the center of the earth
(TOPEX/Poseidon) or a reference elipsoid (Jason-1) to obtain the elevation
of the ocean's surface. Satellite altimetry can be used to obtain tidal
information in the deep ocean where tidal gages are lacking and to
more accurately tune current tidal data along the coasts. Tides can
now be predicted with an accuracy of 2 centimeters anywhere in the deep
ocean.

Many factors determine the magnitude and timing of tides.
First, Considering that a tidal wave is a forced wave controlled by the the
gravitational effects
of the Moon and Sun on the Earth then variations in the positioning
of the Moon and Sun relative to the
Earth will cause consistant predictable tidal fluctuations. Second, the
coriolis effect produced by the rotation of the earth and the constriction
of the wave by ocean basins transforms the wave into a kelvin wave(amphidromic
system)
that
rotates
clockwise in the northern hemisphere and counterclockwise in
the
southern
hemisphere. Basin geometry influences the following:

Size of the amphidromic system (size
and shape of basin): Tides are larger in large basins.

Position of amphidromic point relative
to the coast: Tides increase with distance from the amphidromic point,
where the tidal range is zero.

Width of the continental margin1:
Wide, shallow margins increase the amplitude of the wave.

Size and orientation of embayments:
Resonance within an elongate embayment, such as the Bay of Fundy can amplify
the wave height.

Variations in ocean depth which can
slow and distorts the wave

Supperimposed on astronomical tides are the effects of
local pressure and wind conditions that can depress or buldge the water's
surface
or pile up water onshore. Unlike astromonical variations, climatic variation
add the less predictable element to tides that are experienced during storm
surges.

1 Predicted
ocean tides are only 50 cm. Higher tides are caused by amplification
over broad continental shelves and funnel shaped embayments, and by
resonance in a basin.